Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,4,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.83209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.0000 | 1.29588 | 0.647939 | − | 0.761692i | \(-0.275631\pi\) | ||||
0.647939 | + | 0.761692i | \(0.275631\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −74.0000 | −1.57876 | −0.789381 | − | 0.613904i | \(-0.789598\pi\) | ||||
−0.789381 | + | 0.613904i | \(0.789598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −42.0000 | −0.722957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.0000 | 1.16988 | 0.584939 | − | 0.811077i | \(-0.301118\pi\) | ||||
0.584939 | + | 0.811077i | \(0.301118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −72.0000 | −0.748176 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.00000 | −0.0725268 | −0.0362634 | − | 0.999342i | \(-0.511546\pi\) | ||||
−0.0362634 | + | 0.999342i | \(0.511546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −138.000 | −0.883654 | −0.441827 | − | 0.897100i | \(-0.645669\pi\) | ||||
−0.441827 | + | 0.897100i | \(0.645669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −80.0000 | −0.463498 | −0.231749 | − | 0.972776i | \(-0.574445\pi\) | ||||
−0.231749 | + | 0.972776i | \(0.574445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −84.0000 | −0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 336.000 | 1.62270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0000 | 0.133296 | 0.0666482 | − | 0.997777i | \(-0.478769\pi\) | ||||
0.0666482 | + | 0.997777i | \(0.478769\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 222.000 | 0.911499 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 282.000 | 1.07417 | 0.537085 | − | 0.843528i | \(-0.319525\pi\) | ||||
0.537085 | + | 0.843528i | \(0.319525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.0141859 | −0.00709296 | − | 0.999975i | \(-0.502258\pi\) | ||||
−0.00709296 | + | 0.999975i | \(0.502258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 126.000 | 0.417399 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −240.000 | −0.744843 | −0.372421 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372421 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 233.000 | 0.679300 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −246.000 | −0.675429 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −130.000 | −0.336922 | −0.168461 | − | 0.985708i | \(-0.553880\pi\) | ||||
−0.168461 | + | 0.985708i | \(0.553880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 392.000 | 0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −596.000 | −1.31513 | −0.657564 | − | 0.753398i | \(-0.728413\pi\) | ||||
−0.657564 | + | 0.753398i | \(0.728413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −218.000 | −0.457574 | −0.228787 | − | 0.973476i | \(-0.573476\pi\) | ||||
−0.228787 | + | 0.973476i | \(0.573476\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 216.000 | 0.431959 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1036.00 | −1.97692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 436.000 | 0.795013 | 0.397507 | − | 0.917599i | \(-0.369876\pi\) | ||||
0.397507 | + | 0.917599i | \(0.369876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.0000 | 0.0418733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −856.000 | −1.43082 | −0.715412 | − | 0.698703i | \(-0.753761\pi\) | ||||
−0.715412 | + | 0.698703i | \(0.753761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −998.000 | −1.60010 | −0.800048 | − | 0.599935i | \(-0.795193\pi\) | ||||
−0.800048 | + | 0.599935i | \(0.795193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −213.000 | −0.327935 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 672.000 | 0.994565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.0000 | 0.0455732 | 0.0227866 | − | 0.999740i | \(-0.492746\pi\) | ||||
0.0227866 | + | 0.999740i | \(0.492746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1508.00 | 1.99427 | 0.997136 | − | 0.0756351i | \(-0.0240984\pi\) | ||||
0.997136 | + | 0.0756351i | \(0.0240984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1148.00 | 1.46492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 414.000 | 0.510178 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −246.000 | −0.292988 | −0.146494 | − | 0.989212i | \(-0.546799\pi\) | ||||
−0.146494 | + | 0.989212i | \(0.546799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1776.00 | −2.04588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 240.000 | 0.267600 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1288.00 | −1.39101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 866.000 | 0.906484 | 0.453242 | − | 0.891387i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891387i | \(0.350267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 252.000 | 0.255828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 270.000 | 0.266000 | 0.133000 | − | 0.991116i | \(-0.457539\pi\) | ||||
0.133000 | + | 0.991116i | \(0.457539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1496.00 | 1.43112 | 0.715560 | − | 0.698552i | \(-0.246172\pi\) | ||||
0.715560 | + | 0.698552i | \(0.246172\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1008.00 | −0.936864 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1692.00 | 1.52871 | 0.764354 | − | 0.644797i | \(-0.223058\pi\) | ||||
0.764354 | + | 0.644797i | \(0.223058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 406.000 | 0.356768 | 0.178384 | − | 0.983961i | \(-0.442913\pi\) | ||||
0.178384 | + | 0.983961i | \(0.442913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −90.0000 | −0.0769588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 786.000 | 0.654342 | 0.327171 | − | 0.944965i | \(-0.393905\pi\) | ||||
0.327171 | + | 0.944965i | \(0.393905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −112.000 | −0.0908179 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −666.000 | −0.526254 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1968.00 | 1.51602 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −846.000 | −0.620173 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1744.00 | −1.21854 | −0.609272 | − | 0.792962i | \(-0.708538\pi\) | ||||
−0.609272 | + | 0.792962i | \(0.708538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 0.00819024 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −652.000 | −0.434851 | −0.217426 | − | 0.976077i | \(-0.569766\pi\) | ||||
−0.217426 | + | 0.976077i | \(0.569766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2208.00 | −1.43953 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −378.000 | −0.240986 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1530.00 | 0.954137 | 0.477068 | − | 0.878866i | \(-0.341699\pi\) | ||||
0.477068 | + | 0.878866i | \(0.341699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −516.000 | −0.314867 | −0.157434 | − | 0.987530i | \(-0.550322\pi\) | ||||
−0.157434 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 720.000 | 0.430035 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2072.00 | −1.21167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1932.00 | −1.10651 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −699.000 | −0.392194 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1342.00 | 0.737859 | 0.368929 | − | 0.929457i | \(-0.379724\pi\) | ||||
0.368929 | + | 0.929457i | \(0.379724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 424.000 | 0.228507 | 0.114254 | − | 0.993452i | \(-0.463552\pi\) | ||||
0.114254 | + | 0.993452i | \(0.463552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 738.000 | 0.389959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1120.00 | −0.580391 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 262.000 | 0.133184 | 0.0665920 | − | 0.997780i | \(-0.478787\pi\) | ||||
0.0665920 | + | 0.997780i | \(0.478787\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 390.000 | 0.194522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.000 | −0.0939858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2292.00 | 1.10137 | 0.550685 | − | 0.834713i | \(-0.314367\pi\) | ||||
0.550685 | + | 0.834713i | \(0.314367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1176.00 | −0.554857 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1896.00 | 0.878544 | 0.439272 | − | 0.898354i | \(-0.355236\pi\) | ||||
0.439272 | + | 0.898354i | \(0.355236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3279.00 | 1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −828.000 | −0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2874.00 | −1.26304 | −0.631521 | − | 0.775359i | \(-0.717569\pi\) | ||||
−0.631521 | + | 0.775359i | \(0.717569\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1704.00 | 0.736059 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1788.00 | 0.759290 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1188.00 | 0.496063 | 0.248032 | − | 0.968752i | \(-0.420216\pi\) | ||||
0.248032 | + | 0.968752i | \(0.420216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3474.00 | −1.42663 | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700843i | \(0.752808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 654.000 | 0.264181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 420.000 | 0.166914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2296.00 | 0.897862 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −648.000 | −0.249392 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192.000 | −0.0727363 | −0.0363681 | − | 0.999338i | \(-0.511579\pi\) | ||||
−0.0363681 | + | 0.999338i | \(0.511579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4802.00 | 1.79096 | 0.895481 | − | 0.445100i | \(-0.146832\pi\) | ||||
0.895481 | + | 0.445100i | \(0.146832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3108.00 | 1.14138 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1518.00 | 0.549000 | 0.274500 | − | 0.961587i | \(-0.411488\pi\) | ||||
0.274500 | + | 0.961587i | \(0.411488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5128.00 | −1.82670 | −0.913352 | − | 0.407170i | \(-0.866516\pi\) | ||||
−0.913352 | + | 0.407170i | \(0.866516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1308.00 | −0.459001 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3312.00 | −1.14511 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3948.00 | 1.34507 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72.0000 | −0.0241756 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2576.00 | −0.852563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1084.00 | −0.353676 | −0.176838 | − | 0.984240i | \(-0.556587\pi\) | ||||
−0.176838 | + | 0.984240i | \(0.556587\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2568.00 | 0.826087 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −56.0000 | −0.0177636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1920.00 | −0.600636 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2994.00 | 0.923816 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6068.00 | −1.84696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −688.000 | −0.206600 | −0.103300 | − | 0.994650i | \(-0.532940\pi\) | ||||
−0.103300 | + | 0.994650i | \(0.532940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 639.000 | 0.189333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4812.00 | −1.40698 | −0.703488 | − | 0.710707i | \(-0.748375\pi\) | ||||
−0.703488 | + | 0.710707i | \(0.748375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2494.00 | 0.719686 | 0.359843 | − | 0.933013i | \(-0.382830\pi\) | ||||
0.359843 | + | 0.933013i | \(0.382830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2016.00 | −0.574212 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 698.000 | 0.196255 | 0.0981277 | − | 0.995174i | \(-0.468715\pi\) | ||||
0.0981277 | + | 0.995174i | \(0.468715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3360.00 | −0.932690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −96.0000 | −0.0263117 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6320.00 | 1.71049 | 0.855244 | − | 0.518225i | \(-0.173407\pi\) | ||||
0.855244 | + | 0.518225i | \(0.173407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6510.00 | −1.74002 | −0.870012 | − | 0.493030i | \(-0.835889\pi\) | ||||
−0.870012 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3262.00 | 0.850619 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6808.00 | 1.75378 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4524.00 | −1.15139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −628.000 | −0.157924 | −0.0789622 | − | 0.996878i | \(-0.525161\pi\) | ||||
−0.0789622 | + | 0.996878i | \(0.525161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224.000 | −0.0556631 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3444.00 | −0.845771 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4862.00 | −1.18009 | −0.590045 | − | 0.807370i | \(-0.700890\pi\) | ||||
−0.590045 | + | 0.807370i | \(0.700890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 720.000 | 0.172736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1242.00 | −0.294551 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5816.00 | −1.36361 | −0.681806 | − | 0.731533i | \(-0.738805\pi\) | ||||
−0.681806 | + | 0.731533i | \(0.738805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1820.00 | −0.421893 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 738.000 | 0.169157 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3526.00 | 0.799197 | 0.399599 | − | 0.916690i | \(-0.369150\pi\) | ||||
0.399599 | + | 0.916690i | \(0.369150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 256.000 | 0.0573834 | 0.0286917 | − | 0.999588i | \(-0.490866\pi\) | ||||
0.0286917 | + | 0.999588i | \(0.490866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5328.00 | 1.18119 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1988.00 | 0.435931 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 142.000 | 0.0308013 | 0.0154006 | − | 0.999881i | \(-0.495098\pi\) | ||||
0.0154006 | + | 0.999881i | \(0.495098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −720.000 | −0.154499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8842.00 | 1.87712 | 0.938558 | − | 0.345122i | \(-0.112162\pi\) | ||||
0.938558 | + | 0.345122i | \(0.112162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7180.00 | 1.50815 | 0.754075 | − | 0.656788i | \(-0.228085\pi\) | ||||
0.754075 | + | 0.656788i | \(0.228085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3864.00 | 0.803100 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6768.00 | 1.39199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1811.00 | 0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2598.00 | −0.523359 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7374.00 | 1.47029 | 0.735143 | − | 0.677912i | \(-0.237115\pi\) | ||||
0.735143 | + | 0.677912i | \(0.237115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8344.00 | −1.64680 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −756.000 | −0.147702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 592.000 | 0.114502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −96.0000 | −0.0183832 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −810.000 | −0.153575 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3052.00 | −0.572974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1500.00 | −0.278858 | −0.139429 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139429 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4488.00 | −0.826257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7608.00 | 1.38717 | 0.693585 | − | 0.720374i | \(-0.256030\pi\) | ||||
0.693585 | + | 0.720374i | \(0.256030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4758.00 | −0.859227 | −0.429614 | − | 0.903013i | \(-0.641350\pi\) | ||||
−0.429614 | + | 0.903013i | \(0.641350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3024.00 | 0.540899 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4374.00 | 0.774979 | 0.387489 | − | 0.921874i | \(-0.373342\pi\) | ||||
0.387489 | + | 0.921874i | \(0.373342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3864.00 | −0.678190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5076.00 | −0.882600 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7544.00 | −1.29956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5254.00 | −0.896737 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1218.00 | −0.205980 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5760.00 | −0.965225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7804.00 | 1.29591 | 0.647956 | − | 0.761678i | \(-0.275624\pi\) | ||||
0.647956 | + | 0.761678i | \(0.275624\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 270.000 | 0.0444322 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6104.00 | 0.995514 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5106.00 | 0.825346 | 0.412673 | − | 0.910879i | \(-0.364595\pi\) | ||||
0.412673 | + | 0.910879i | \(0.364595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2358.00 | −0.377785 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2240.00 | −0.355727 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2640.00 | −0.415588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 336.000 | 0.0524337 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4716.00 | 0.729591 | 0.364796 | − | 0.931088i | \(-0.381139\pi\) | ||||
0.364796 | + | 0.931088i | \(0.381139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7302.00 | 1.11996 | 0.559982 | − | 0.828505i | \(-0.310808\pi\) | ||||
0.559982 | + | 0.828505i | \(0.310808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1998.00 | 0.303833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4382.00 | −0.660709 | −0.330355 | − | 0.943857i | \(-0.607168\pi\) | ||||
−0.330355 | + | 0.943857i | \(0.607168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11984.0 | −1.79168 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5904.00 | −0.875274 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7224.00 | −1.06203 | −0.531014 | − | 0.847363i | \(-0.678189\pi\) | ||||
−0.531014 | + | 0.847363i | \(0.678189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1641.00 | 0.237273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13972.0 | −2.00364 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1408.00 | −0.200264 | −0.100132 | − | 0.994974i | \(-0.531927\pi\) | ||||
−0.100132 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2538.00 | 0.358057 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3120.00 | −0.436610 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1714.00 | −0.237929 | −0.118965 | − | 0.992899i | \(-0.537957\pi\) | ||||
−0.118965 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2268.00 | 0.312317 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10212.0 | 1.39508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −884.000 | −0.119810 | −0.0599051 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599051 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5232.00 | 0.703526 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10368.0 | −1.38324 | −0.691619 | − | 0.722263i | \(-0.743102\pi\) | ||||
−0.691619 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9408.00 | 1.24539 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36.0000 | −0.00472864 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 398.000 | 0.0518751 | 0.0259375 | − | 0.999664i | \(-0.491743\pi\) | ||||
0.0259375 | + | 0.999664i | \(0.491743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −656.000 | −0.0848474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1956.00 | 0.251061 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 448.000 | 0.0570666 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5098.00 | −0.644487 | −0.322243 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322243 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6624.00 | 0.831115 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10002.0 | 1.24558 | 0.622788 | − | 0.782391i | \(-0.286000\pi\) | ||||
0.622788 | + | 0.782391i | \(0.286000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5920.00 | 0.731752 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1134.00 | 0.139133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 840.000 | 0.102303 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9270.00 | −1.12071 | −0.560357 | − | 0.828251i | \(-0.689336\pi\) | ||||
−0.560357 | + | 0.828251i | \(0.689336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4590.00 | −0.550871 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14304.0 | −1.70425 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21112.0 | 2.49722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1548.00 | 0.181789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6516.00 | 0.759731 | 0.379866 | − | 0.925042i | \(-0.375970\pi\) | ||||
0.379866 | + | 0.925042i | \(0.375970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2626.00 | −0.303999 | −0.151999 | − | 0.988381i | \(-0.548571\pi\) | ||||
−0.151999 | + | 0.988381i | \(0.548571\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2160.00 | −0.248281 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5822.00 | 0.664491 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5232.00 | −0.592961 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6216.00 | 0.699560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4304.00 | 0.481012 | 0.240506 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240506 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11794.0 | 1.30897 | 0.654484 | − | 0.756076i | \(-0.272886\pi\) | ||||
0.654484 | + | 0.756076i | \(0.272886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5796.00 | 0.638844 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 736.000 | 0.0805667 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5544.00 | 0.602735 | 0.301368 | − | 0.953508i | \(-0.402557\pi\) | ||||
0.301368 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2097.00 | 0.226433 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3788.00 | 0.406260 | 0.203130 | − | 0.979152i | \(-0.434889\pi\) | ||||
0.203130 | + | 0.979152i | \(0.434889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3444.00 | −0.366879 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4026.00 | −0.426003 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13342.0 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7896.00 | 0.824408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1272.00 | −0.131929 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24864.0 | −2.56185 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4390.00 | −0.449356 | −0.224678 | − | 0.974433i | \(-0.572133\pi\) | ||||
−0.224678 | + | 0.974433i | \(0.572133\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2214.00 | −0.225143 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5798.00 | 0.585770 | 0.292885 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292885 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14656.0 | 1.47111 | 0.735553 | − | 0.677467i | \(-0.236922\pi\) | ||||
0.735553 | + | 0.677467i | \(0.236922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3360.00 | 0.335089 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8412.00 | −0.833535 | −0.416768 | − | 0.909013i | \(-0.636837\pi\) | ||||
−0.416768 | + | 0.909013i | \(0.636837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10464.0 | 1.03024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −786.000 | −0.0768938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −112.000 | −0.0108875 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6532.00 | −0.630966 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1170.00 | −0.112307 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14848.0 | −1.41633 | −0.708165 | − | 0.706047i | \(-0.750477\pi\) | ||||
−0.708165 | + | 0.706047i | \(0.750477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2220.00 | −0.210443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 576.000 | 0.0542627 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12124.0 | 1.13510 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18568.0 | −1.72771 | −0.863857 | − | 0.503738i | \(-0.831958\pi\) | ||||
−0.863857 | + | 0.503738i | \(0.831958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6876.00 | −0.635876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14364.0 | 1.32024 | 0.660120 | − | 0.751160i | \(-0.270505\pi\) | ||||
0.660120 | + | 0.751160i | \(0.270505\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11316.0 | −1.03377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3528.00 | 0.320347 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20544.0 | −1.85417 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21660.0 | −1.94316 | −0.971578 | − | 0.236720i | \(-0.923928\pi\) | ||||
−0.971578 | + | 0.236720i | \(0.923928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5688.00 | −0.507228 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17112.0 | 1.51687 | 0.758436 | − | 0.651748i | \(-0.225964\pi\) | ||||
0.758436 | + | 0.651748i | \(0.225964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3780.00 | 0.333085 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9837.00 | −0.861689 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11478.0 | 0.999516 | 0.499758 | − | 0.866165i | \(-0.333422\pi\) | ||||
0.499758 | + | 0.866165i | \(0.333422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23952.0 | −2.07353 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20944.0 | 1.79204 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6720.00 | −0.571654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8622.00 | 0.729217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13114.0 | 1.10275 | 0.551377 | − | 0.834256i | \(-0.314103\pi\) | ||||
0.551377 | + | 0.834256i | \(0.314103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4508.00 | 0.376905 | 0.188452 | − | 0.982082i | \(-0.439653\pi\) | ||||
0.188452 | + | 0.982082i | \(0.439653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5112.00 | −0.424964 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6560.00 | −0.542235 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12103.0 | −0.994740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5364.00 | −0.438376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20868.0 | −1.69586 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23688.0 | 1.91425 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3564.00 | −0.286402 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6524.00 | 0.521352 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22950.0 | 1.82384 | 0.911920 | − | 0.410368i | \(-0.134600\pi\) | ||||
0.911920 | + | 0.410368i | \(0.134600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10422.0 | 0.823666 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5684.00 | 0.446745 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6580.00 | 0.514334 | 0.257167 | − | 0.966367i | \(-0.417211\pi\) | ||||
0.257167 | + | 0.966367i | \(0.417211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1962.00 | −0.152525 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12696.0 | 0.981611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 768.000 | 0.0590573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1260.00 | −0.0963676 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7046.00 | 0.535994 | 0.267997 | − | 0.963420i | \(-0.413638\pi\) | ||||
0.267997 | + | 0.963420i | \(0.413638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 296.000 | 0.0223962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6888.00 | −0.518381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8252.00 | −0.617727 | −0.308864 | − | 0.951106i | \(-0.599949\pi\) | ||||
−0.308864 | + | 0.951106i | \(0.599949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11004.0 | 0.819366 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1944.00 | 0.143986 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6838.00 | −0.503803 | −0.251901 | − | 0.967753i | \(-0.581056\pi\) | ||||
−0.251901 | + | 0.967753i | \(0.581056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23316.0 | −1.70883 | −0.854417 | − | 0.519588i | \(-0.826085\pi\) | ||||
−0.854417 | + | 0.519588i | \(0.826085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 576.000 | 0.0419943 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −568.000 | −0.0411952 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10558.0 | −0.761760 | −0.380880 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14406.0 | −1.03401 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36192.0 | 2.58433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3640.00 | −0.258582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9324.00 | −0.658974 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1028.00 | −0.0722830 | −0.0361415 | − | 0.999347i | \(-0.511507\pi\) | ||||
−0.0361415 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7360.00 | 0.514879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4554.00 | −0.316965 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1202.00 | 0.0832382 | 0.0416191 | − | 0.999134i | \(-0.486748\pi\) | ||||
0.0416191 | + | 0.999134i | \(0.486748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27552.0 | 1.89836 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15384.0 | 1.05465 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3576.00 | 0.243926 | 0.121963 | − | 0.992535i | \(-0.461081\pi\) | ||||
0.121963 | + | 0.992535i | \(0.461081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8650.00 | 0.587090 | 0.293545 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293545 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3924.00 | 0.265004 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7658.00 | −0.514615 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12656.0 | −0.846279 | −0.423139 | − | 0.906065i | \(-0.639072\pi\) | ||||
−0.423139 | + | 0.906065i | \(0.639072\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9936.00 | 0.661128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17760.0 | 1.17593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3298.00 | −0.217300 | −0.108650 | − | 0.994080i | \(-0.534653\pi\) | ||||
−0.108650 | + | 0.994080i | \(0.534653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11844.0 | −0.776579 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5370.00 | 0.350386 | 0.175193 | − | 0.984534i | \(-0.443945\pi\) | ||||
0.175193 | + | 0.984534i | \(0.443945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16220.0 | 1.05321 | 0.526605 | − | 0.850110i | \(-0.323465\pi\) | ||||
0.526605 | + | 0.850110i | \(0.323465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 216.000 | 0.0139578 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5904.00 | −0.379677 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7728.00 | 0.492227 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2460.00 | 0.155941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20360.0 | 1.28450 | 0.642249 | − | 0.766496i | \(-0.278001\pi\) | ||||
0.642249 | + | 0.766496i | \(0.278001\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3252.00 | 0.204195 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24416.0 | −1.52586 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17242.0 | −1.07245 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7704.00 | −0.476941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14498.0 | 0.893349 | 0.446674 | − | 0.894697i | \(-0.352608\pi\) | ||||
0.446674 | + | 0.894697i | \(0.352608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21612.0 | −1.32550 | −0.662748 | − | 0.748842i | \(-0.730610\pi\) | ||||
−0.662748 | + | 0.748842i | \(0.730610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 168.000 | 0.0102558 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12184.0 | −0.740344 | −0.370172 | − | 0.928963i | \(-0.620701\pi\) | ||||
−0.370172 | + | 0.928963i | \(0.620701\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16688.0 | −1.00934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5760.00 | 0.346778 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28122.0 | −1.68530 | −0.842648 | − | 0.538464i | \(-0.819005\pi\) | ||||
−0.842648 | + | 0.538464i | \(0.819005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9128.00 | −0.544520 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8982.00 | −0.533366 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5700.00 | 0.336935 | 0.168468 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168468 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29458.0 | −1.73341 | −0.866705 | − | 0.498822i | \(-0.833766\pi\) | ||||
−0.866705 | + | 0.498822i | \(0.833766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18204.0 | 1.06634 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30912.0 | −1.80258 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1104.00 | 0.0640885 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2064.00 | 0.119281 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6104.00 | −0.351181 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19810.0 | 1.13465 | 0.567325 | − | 0.823494i | \(-0.307978\pi\) | ||||
0.567325 | + | 0.823494i | \(0.307978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1917.00 | −0.109312 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10450.0 | −0.593244 | −0.296622 | − | 0.954995i | \(-0.595860\pi\) | ||||
−0.296622 | + | 0.954995i | \(0.595860\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20784.0 | 1.17469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14436.0 | 0.812318 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23300.0 | −1.30534 | −0.652672 | − | 0.757641i | \(-0.726352\pi\) | ||||
−0.652672 | + | 0.757641i | \(0.726352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21420.0 | 1.19477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7482.00 | −0.415511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9620.00 | 0.531920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14212.0 | 0.782417 | 0.391208 | − | 0.920302i | \(-0.372057\pi\) | ||||
0.391208 | + | 0.920302i | \(0.372057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6048.00 | 0.331522 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7224.00 | −0.394276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23124.0 | 1.25665 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2094.00 | −0.113308 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15978.0 | −0.860885 | −0.430443 | − | 0.902618i | \(-0.641643\pi\) | ||||
−0.430443 | + | 0.902618i | \(0.641643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2760.00 | −0.148073 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10080.0 | 0.538489 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6480.00 | 0.344704 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8866.00 | −0.469633 | −0.234816 | − | 0.972040i | \(-0.575449\pi\) | ||||
−0.234816 | + | 0.972040i | \(0.575449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 288.000 | 0.0151911 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 640.000 | 0.0336160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29008.0 | −1.51726 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18960.0 | −0.987551 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7760.00 | −0.402502 | −0.201251 | − | 0.979540i | \(-0.564501\pi\) | ||||
−0.201251 | + | 0.979540i | \(0.564501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35904.0 | 1.85456 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19530.0 | 1.00460 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9798.00 | −0.501915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13080.0 | −0.667277 | −0.333638 | − | 0.942701i | \(-0.608276\pi\) | ||||
−0.333638 | + | 0.942701i | \(0.608276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −328.000 | −0.0165958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16934.0 | 0.853304 | 0.426652 | − | 0.904416i | \(-0.359693\pi\) | ||||
0.426652 | + | 0.904416i | \(0.359693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9786.00 | −0.491105 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12208.0 | 0.610159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7060.00 | 0.351429 | 0.175715 | − | 0.984441i | \(-0.443776\pi\) | ||||
0.175715 | + | 0.984441i | \(0.443776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20424.0 | −1.01254 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12520.0 | 0.618189 | 0.309094 | − | 0.951031i | \(-0.399974\pi\) | ||||
0.309094 | + | 0.951031i | \(0.399974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18788.0 | 0.923945 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13572.0 | 0.664757 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40608.0 | 1.98102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9792.00 | 0.475786 | 0.237893 | − | 0.971291i | \(-0.423543\pi\) | ||||
0.237893 | + | 0.971291i | \(0.423543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1884.00 | 0.0911777 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5936.00 | 0.286137 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13166.0 | 0.632135 | 0.316068 | − | 0.948737i | \(-0.397637\pi\) | ||||
0.316068 | + | 0.948737i | \(0.397637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 672.000 | 0.0321371 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23222.0 | −1.10617 | −0.553086 | − | 0.833124i | \(-0.686550\pi\) | ||||
−0.553086 | + | 0.833124i | \(0.686550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9744.00 | 0.462328 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10332.0 | 0.488306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44104.0 | 2.07628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39934.0 | −1.87264 | −0.936318 | − | 0.351154i | \(-0.885789\pi\) | ||||
−0.936318 | + | 0.351154i | \(0.885789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14586.0 | 0.681325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17106.0 | −0.795938 | −0.397969 | − | 0.917399i | \(-0.630285\pi\) | ||||
−0.397969 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5680.00 | −0.263267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2160.00 | −0.0997292 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25944.0 | −1.19325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23968.0 | −1.09813 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3726.00 | 0.170059 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3668.00 | 0.166773 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9956.00 | 0.450944 | 0.225472 | − | 0.974250i | \(-0.427608\pi\) | ||||
0.225472 | + | 0.974250i | \(0.427608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17448.0 | 0.787282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18864.0 | 0.847948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16132.0 | 0.722401 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5460.00 | 0.243580 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9130.00 | −0.405773 | −0.202887 | − | 0.979202i | \(-0.565032\pi\) | ||||
−0.202887 | + | 0.979202i | \(0.565032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19680.0 | −0.871375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2214.00 | −0.0976627 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27944.0 | −1.22805 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2688.00 | −0.117689 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10578.0 | −0.461417 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11482.0 | 0.498993 | 0.249497 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249497 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4612.00 | −0.199691 | −0.0998454 | − | 0.995003i | \(-0.531835\pi\) | ||||
−0.0998454 | + | 0.995003i | \(0.531835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −768.000 | −0.0331303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32088.0 | 1.37913 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 368.000 | 0.0157585 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15984.0 | −0.681961 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35010.0 | −1.48826 | −0.744128 | − | 0.668038i | \(-0.767135\pi\) | ||||
−0.744128 | + | 0.668038i | \(0.767135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13688.0 | −0.579749 | −0.289875 | − | 0.957065i | \(-0.593614\pi\) | ||||
−0.289875 | + | 0.957065i | \(0.593614\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5964.00 | −0.251685 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11668.0 | −0.490612 | −0.245306 | − | 0.969446i | \(-0.578888\pi\) | ||||
−0.245306 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29306.0 | −1.22779 | −0.613896 | − | 0.789387i | \(-0.710399\pi\) | ||||
−0.613896 | + | 0.789387i | \(0.710399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −426.000 | −0.0177831 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19106.0 | 0.794698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26544.0 | 1.10011 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2160.00 | 0.0892001 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2664.00 | 0.109620 | 0.0548102 | − | 0.998497i | \(-0.482545\pi\) | ||||
0.0548102 | + | 0.998497i | \(0.482545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5345.00 | −0.219156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26526.0 | −1.08375 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45906.0 | 1.86889 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13128.0 | −0.532566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21540.0 | −0.870731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −240.000 | −0.00966756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26030.0 | 1.04484 | 0.522421 | − | 0.852688i | \(-0.325029\pi\) | ||||
0.522421 | + | 0.852688i | \(0.325029\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11592.0 | −0.463670 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44202.0 | 1.76186 | 0.880929 | − | 0.473249i | \(-0.156919\pi\) | ||||
0.880929 | + | 0.473249i | \(0.156919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32748.0 | 1.30075 | 0.650377 | − | 0.759612i | \(-0.274611\pi\) | ||||
0.650377 | + | 0.759612i | \(0.274611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20304.0 | −0.803668 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45344.0 | −1.78856 | −0.894280 | − | 0.447507i | \(-0.852312\pi\) | ||||
−0.894280 | + | 0.447507i | \(0.852312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40236.0 | −1.58158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5433.00 | −0.212819 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 896.000 | 0.0349767 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32264.0 | −1.25514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7794.00 | 0.302161 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18144.0 | −0.701005 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8778.00 | −0.337984 | −0.168992 | − | 0.985617i | \(-0.554051\pi\) | ||||
−0.168992 | + | 0.985617i | \(0.554051\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22122.0 | −0.848870 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4142.00 | −0.158397 | −0.0791984 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791984 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22076.0 | −0.841355 | −0.420678 | − | 0.907210i | \(-0.638208\pi\) | ||||
−0.420678 | + | 0.907210i | \(0.638208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25032.0 | 0.950781 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40376.0 | 1.52840 | 0.764201 | − | 0.644978i | \(-0.223133\pi\) | ||||
0.764201 | + | 0.644978i | \(0.223133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41856.0 | −1.57908 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2268.00 | 0.0852759 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22080.0 | 0.827412 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16632.0 | 0.621169 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1776.00 | −0.0661080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11040.0 | 0.409571 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10660.0 | −0.394158 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 288.000 | 0.0106136 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48636.0 | −1.78643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26396.0 | 0.966334 | 0.483167 | − | 0.875528i | \(-0.339486\pi\) | ||||
0.483167 | + | 0.875528i | \(0.339486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2430.00 | 0.0886667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24368.0 | −0.886222 | −0.443111 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443111 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42224.0 | 1.53057 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9156.00 | 0.330807 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15648.0 | −0.563514 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5096.00 | 0.182918 | 0.0914589 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914589 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4500.00 | 0.160999 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 63344.0 | 2.25893 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2130.00 | 0.0757124 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13464.0 | 0.477040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18494.0 | −0.653142 | −0.326571 | − | 0.945173i | \(-0.605893\pi\) | ||||
−0.326571 | + | 0.945173i | \(0.605893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21436.0 | −0.754604 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22824.0 | −0.800883 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32144.0 | 1.12430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33222.0 | −1.15829 | −0.579144 | − | 0.815225i | \(-0.696613\pi\) | ||||
−0.579144 | + | 0.815225i | \(0.696613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14274.0 | 0.496075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27846.0 | 0.964669 | 0.482335 | − | 0.875987i | \(-0.339789\pi\) | ||||
0.482335 | + | 0.875987i | \(0.339789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2256.00 | −0.0779061 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9072.00 | −0.312288 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41052.0 | −1.40867 | −0.704335 | − | 0.709868i | \(-0.748755\pi\) | ||||
−0.704335 | + | 0.709868i | \(0.748755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 73852.0 | 2.52617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13122.0 | −0.447434 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5706.00 | 0.193951 | 0.0969756 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969756 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2688.00 | −0.0910802 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11592.0 | 0.391553 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36720.0 | 1.23644 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23391.0 | −0.785170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15228.0 | 0.509570 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 67228.0 | 2.24264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39352.0 | 1.30866 | 0.654330 | − | 0.756209i | \(-0.272951\pi\) | ||||
0.654330 | + | 0.756209i | \(0.272951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22632.0 | 0.750304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33180.0 | 1.09660 | 0.548299 | − | 0.836282i | \(-0.315276\pi\) | ||||
0.548299 | + | 0.836282i | \(0.315276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12384.0 | −0.408030 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15762.0 | 0.517731 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4014.00 | −0.131442 | −0.0657212 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657212 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6888.00 | −0.224864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3654.00 | 0.118923 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20328.0 | −0.659575 | −0.329788 | − | 0.944055i | \(-0.606977\pi\) | ||||
−0.329788 | + | 0.944055i | \(0.606977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21252.0 | 0.687457 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17280.0 | 0.557273 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 0.00102886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11728.0 | −0.375936 | −0.187968 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187968 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23412.0 | −0.748195 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71792.0 | −2.28740 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50974.0 | 1.61922 | 0.809610 | − | 0.586968i | \(-0.199679\pi\) | ||||
0.809610 | + | 0.586968i | \(0.199679\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −810.000 | −0.0256529 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 48.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 144.4.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 24.4.a.a.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1200.4.f.p.49.2 | 2 | |||
5.3 | odd | 4 | 1200.4.f.p.49.1 | 2 | |||
5.4 | even | 2 | 1200.4.a.u.1.1 | 1 | |||
7.6 | odd | 2 | 2352.4.a.w.1.1 | 1 | |||
8.3 | odd | 2 | 192.4.a.a.1.1 | 1 | |||
8.5 | even | 2 | 192.4.a.g.1.1 | 1 | |||
12.11 | even | 2 | 72.4.a.b.1.1 | 1 | |||
16.3 | odd | 4 | 768.4.d.o.385.2 | 2 | |||
16.5 | even | 4 | 768.4.d.b.385.2 | 2 | |||
16.11 | odd | 4 | 768.4.d.o.385.1 | 2 | |||
16.13 | even | 4 | 768.4.d.b.385.1 | 2 | |||
20.3 | even | 4 | 600.4.f.b.49.2 | 2 | |||
20.7 | even | 4 | 600.4.f.b.49.1 | 2 | |||
20.19 | odd | 2 | 600.4.a.h.1.1 | 1 | |||
24.5 | odd | 2 | 576.4.a.v.1.1 | 1 | |||
24.11 | even | 2 | 576.4.a.u.1.1 | 1 | |||
28.27 | even | 2 | 1176.4.a.a.1.1 | 1 | |||
36.7 | odd | 6 | 648.4.i.b.433.1 | 2 | |||
36.11 | even | 6 | 648.4.i.k.433.1 | 2 | |||
36.23 | even | 6 | 648.4.i.k.217.1 | 2 | |||
36.31 | odd | 6 | 648.4.i.b.217.1 | 2 | |||
60.23 | odd | 4 | 1800.4.f.q.649.2 | 2 | |||
60.47 | odd | 4 | 1800.4.f.q.649.1 | 2 | |||
60.59 | even | 2 | 1800.4.a.bg.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
48.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
72.4.a.b.1.1 | 1 | 12.11 | even | 2 | |||
144.4.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
192.4.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
192.4.a.g.1.1 | 1 | 8.5 | even | 2 | |||
576.4.a.u.1.1 | 1 | 24.11 | even | 2 | |||
576.4.a.v.1.1 | 1 | 24.5 | odd | 2 | |||
600.4.a.h.1.1 | 1 | 20.19 | odd | 2 | |||
600.4.f.b.49.1 | 2 | 20.7 | even | 4 | |||
600.4.f.b.49.2 | 2 | 20.3 | even | 4 | |||
648.4.i.b.217.1 | 2 | 36.31 | odd | 6 | |||
648.4.i.b.433.1 | 2 | 36.7 | odd | 6 | |||
648.4.i.k.217.1 | 2 | 36.23 | even | 6 | |||
648.4.i.k.433.1 | 2 | 36.11 | even | 6 | |||
768.4.d.b.385.1 | 2 | 16.13 | even | 4 | |||
768.4.d.b.385.2 | 2 | 16.5 | even | 4 | |||
768.4.d.o.385.1 | 2 | 16.11 | odd | 4 | |||
768.4.d.o.385.2 | 2 | 16.3 | odd | 4 | |||
1176.4.a.a.1.1 | 1 | 28.27 | even | 2 | |||
1200.4.a.u.1.1 | 1 | 5.4 | even | 2 | |||
1200.4.f.p.49.1 | 2 | 5.3 | odd | 4 | |||
1200.4.f.p.49.2 | 2 | 5.2 | odd | 4 | |||
1800.4.a.bg.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.f.q.649.1 | 2 | 60.47 | odd | 4 | |||
1800.4.f.q.649.2 | 2 | 60.23 | odd | 4 | |||
2352.4.a.w.1.1 | 1 | 7.6 | odd | 2 |